Some results on parabolic evolution equations with infinitely many variables
type: Item
instance of: scholarly article
title: Some results on parabolic evolution equations with infinitely many variables
zbMATH Open document ID: 0628.35044
DOI: 10.1016/0022-0396(87)90196-3
published in: Journal of Differential Equations
publication date: 1987-01-01T00:00:00Z
review text: The author considers the problem (*) \(\Phi_ t=(1/2)Tr(S\Phi_{xx})\), \(\Phi (0,x)=\Phi_ 0(x)\) with S denoting a nuclear positive operator on a separable Hilbert space H, \(\Phi\) being a mapping (0,\(\infty)\times H\to R\) and Tr denoting the trace. Problems of this tpye are of importance in probability theory. The author then proves existence and uniqueness results in problem (*) and extensions of it.
Mathematics Subject Classification ID: 35G10
Mathematics Subject Classification ID: 35K25
zbMATH DE Number: 4021735
zbMATH Keywords: nuclear positive operator
zbMATH Keywords: separable Hilbert space
zbMATH Keywords: existence
zbMATH Keywords: uniqueness
author: Guiseppe Da Prato
reviewed by: Robert L. Taylor
MaRDI profile type: Publication
full work available at URL: 0022-0396(87)90196-3
OpenAlex ID: W1967738686
cites work: Q4746091
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description: scientific article; zbMATH DE number 4021735